Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T04:02:40.269Z Has data issue: false hasContentIssue false
  • English
  • Français

UNIVERSALLY MARKETABLE INSURANCE UNDER MULTIVARIATE MIXTURES

Published online by Cambridge University Press:  24 November 2020

Ambrose Lo ,
Qihe Tang  and
Zhaofeng Tang
Ambrose Lo
Affiliation:
Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA52242, USA, E-Mail: ambrose-lo@uiowa.edu
Qihe Tang
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney, Sydney, NSW2052, Australia Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA52242, USA, E-Mail: qihe.tang@unsw.edu.au; qihe-tang@uiowa.edu
Zhaofeng Tang*
Affiliation:
Model Validation Group, S&P Global Ratings, One Prudential Plaza Suite 3600, 130 East Randolph Street, Chicago, IL60601, USA, E-Mail: zhaofeng.tang@spglobal.com
*
E-Mail: zhaofeng.tang@spglobal.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The study of desirable structural properties that define a marketable insurance contract has been a recurring theme in insurance economic theory and practice. In this article, we develop probabilistic and structural characterizations for insurance indemnities that are universally marketable in the sense that they appeal to all policyholders whose risk preferences respect the convex order. We begin with the univariate case where a given policyholder faces a single risk, then extend our results to the case where multiple risks possessing a certain dependence structure coexist. The non-decreasing and 1-Lipschitz condition, in various forms, is shown to be intimately related to the notion of universal marketability. As the highlight of this article, we propose a multivariate mixture model which not only accommodates a host of dependence structures commonly encountered in practice but is also flexible enough to house a rich class of marketable indemnity schedules.

Keywords

1-LipschitzdependenceindemnitymarketabilitymixturesC02G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 221 - 243
Copyright
© 2020 by Astin Bulletin. All rights reserved

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Block, H.W., Savits, T.H. and Shaked, M. (1985) A concept of negative dependence using stochastic ordering. Statistics & Probability Letters, 3(2), 81–86.10.1016/0167-7152(85)90029-XCrossRefGoogle Scholar
Cai, J., Liu, H. and Wang, R. (2017) Pareto-optimal reinsurance arrangements under general model settings. Insurance: Mathematics and Economics, 77, 24–37.Google Scholar
Cai, J. and Wei, W. (2012) Optimal reinsurance with positively dependent risks. Insurance: Mathematics and Economics, 50(1), 57–63.Google Scholar
Cheung, K.C., Dhaene, J., Lo, A. and Tang, Q. (2014) Reducing risk by merging counter-monotonic risks. Insurance: Mathematics and Economics, 54, 58–65.Google Scholar
Cheung, K.C. and Lo, A. (2017) Characterizations of optimal reinsurance treaties: A cost-benefit approach. Scandinavian Actuarial Journal, 2017(1), 1–28.10.1080/03461238.2015.1054303CrossRefGoogle Scholar
Chi, Y. and Tan, K.S. (2011) Optimal reinsurance under VaR and CVaR risk measures: A simplified approach. ASTIN Bulletin, 41(2), 487–509.Google Scholar
Cochrane, J.H. (2005) Asset Pricing , Revised edition. Princeton, NJ: Princeton University Press.Google Scholar
Denuit, M., Dhaene, J., Goovaerts, M.J. and Kaas, R. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. Chichester, England: Wiley.10.1002/0470016450CrossRefGoogle Scholar
Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. and Vyncke, D. (2002) The concept of comonotonicity in actuarial science and finance: Theory. Insurance: Mathematics and Economics, 31(1), 3–33.Google Scholar
Eeckhoudt, L., Gollier, C. and Schlesinger, H. (2005) Economic and Financial Decisions under Risk. Princeton, NJ: Princeton University Press.10.1515/9781400829217CrossRefGoogle Scholar
Esary, J.D., Proschan, F. and Walkup, D.W. (1967) Association of random variables, with applications. Annals of Mathematical Statistics, 38(5), 1466–1474.10.1214/aoms/1177698701CrossRefGoogle Scholar
He, J., Tang, Q. and Zhang, H. (2016) Risk reducers in convex order. Insurance: Mathematics and Economics, 70, 80–88.Google Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. London, England: Chapman & Hall.Google Scholar
Kuczma, M. (2009) An Introduction to the Theory of Functional Equations and Inequalities: Cauchy’s Equation and Jensen’s Inequality, Second edition. Basel, Switzerland: Birkhäuser.10.1007/978-3-7643-8749-5CrossRefGoogle Scholar
Lo, A. (2017) A Neyman-Pearson perspective on optimal reinsurance with constraints. ASTIN Bulletin, 47(2), 467–499.10.1017/asb.2016.42CrossRefGoogle Scholar
Müller, A. and Stoyan, D. (2002) Comparison Methods for Stochastic Models and Risks. Chichester, England: Wiley.Google Scholar
Puccetti, G. and Scarsini, M. (2010) Multivariate comonotonicity. Journal of Multivariate Analysis, 101(1), 291–304.10.1016/j.jmva.2009.08.003CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J.G. (2007) Stochastic Orders. New York, NY: Springer.10.1007/978-0-387-34675-5CrossRefGoogle Scholar
Young, V.R. (1999) Optimal insurance under Wang’s premium principle. Insurance: Mathematics and Economics, 25(2), 109–122.Google Scholar